Coulomb drag between ballistic one-dimensional electron systems

The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. In this review, we review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, also known as quantum wires, in the absence of inter-wire tunnelling, to focus on these features and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum drag resistance R_D when the one-dimensional subbands of the two quantum wires are aligned and the Fermi wave vector k_F is small, and also an exponential decay of R_D with increasing inter-wire separation, both features confirmed by experimental observations. A crucial difference between the two theoretical models emerges in the temperature dependence of the drag effect. Although the FL theory predicts a linear temperature dependence, the LL theory promises a rich and varied dependence on temperature depending on the relative magnitudes of the energy and length scales of the systems. At very low temperatures, the drag resistance may diverge due to the formation of locked charge density waves. At higher temperatures, it should show a power-law dependence on temperature, R_D ∝ T^x, experimentally confirmed in a narrow temperature range, where x is determined by the Luttinger liquid parameters. The spin degree of freedom plays an important role in the LL theory in predicting the features of the drag effect and is crucial for the interpretation of experimental results. Substantial experimental and theoretical work remains to be done for a comprehensive understanding of one-dimensional Coulomb drag.